h^2+8h=-9

Solution for h^2+8h=-9 equation:

h^2+8h=-9

We move all terms to the left:

h^2+8h-(-9)=0

We add all the numbers together, and all the variables

h^2+8h+9=0

a = 1; b = 8; c = +9;
Δ = b2-4ac
Δ = 82-4·1·9
Δ = 28
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{28}=\sqrt{4*7}=\sqrt{4}*\sqrt{7}=2\sqrt{7}$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{7}}{2*1}=\frac{-8-2\sqrt{7}}{2}
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{7}}{2*1}=\frac{-8+2\sqrt{7}}{2}
$